Emily is 8 years younger than Stephanie. For the last 3 years, Stephanie and Emily have been going to the same school. Ten years ago, Stephanie was 5 times as old as Emily. How old is Stephanie now?
Solution: We can use the given information to write down two equations that describe the ages of Stephanie and Emily. Let Stephanie's current age be $s$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $s = e + 8$ Ten years ago, Stephanie was $s - 10$ years old, and Emily was $e - 10$ years old. The information in the second sentence can be expressed in the following equation: $s - 10 = 5(e - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = s - 8$ . Substituting this into our second equation, we get the equation: $s - 10 = 5($ $(s - 8)$ $ -$ $ 10)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 10 = 5s - 90$ Solving for $s$ , we get: $4 s = 80$ $s = 20$.